The DFG Collaborative Research Center 1026 "Sustainable Manufacturing" publishes a summary of its results in a book of the same title in the open access series by Springer. Edited by Rainer Stark, Günter Seliger, and Jérémy Bonvoisin, the book provides an overview of the state-of-the art in sustainable production, life cycle engineering, and life cycle management. A chapter on mathematical optimization methods by Sebastian Schenker, Ingmar Vierhaus, Ralf Borndörfer, Armin Fügenschuh, and Martin Skutella reports on progress in multicriteria optimization and system dynamics.